Question 1161973
If you reverse the two digits of Emma's age, add 17 and divide by 2, you get Emma's age.
 How old is she?
Let a = the 10's digit of E's age
let b = the units
then
10a + b = E's age
"If you reverse the two digits of Emma's age, add 17 and divide by 2, you get Emma's age."
{{{(10b + a + 17)/2}}} = 10a + b
multiply both sides by 2
10b + a + 17 = 2(10a + b)
10b + a + 17 = 20a = 2b
10b - 2b + 17 = 20a - a
8b + 17 = 19a
Arrange as a standard equation (I put it in my Ti83, looked at the table}
a = {{{(8b+17)/19}}}
(I put y = (8x+17)/19 in my Ti83, looked at the table)
the only single integer solution to this equation is;
a = 3, b = 5
Emma's age is 35
:
:
See if that checks
{{{(10(5) + 3 + 17)/2}}} = 
{{{(50+20)/2}}} = 35